A197432 a(n) = Sum_{k>=0} A030308(n,k)*C(k) where C(k) is the k-th Catalan number (A000108).

0, 1, 1, 2, 2, 3, 3, 4, 5, 6, 6, 7, 7, 8, 8, 9, 14, 15, 15, 16, 16, 17, 17, 18, 19, 20, 20, 21, 21, 22, 22, 23, 42, 43, 43, 44, 44, 45, 45, 46, 47, 48, 48, 49, 49, 50, 50, 51, 56, 57, 57, 58, 58, 59, 59, 60, 61, 62, 62, 63, 63, 64, 64, 65

Offset

0,4

Comments

Replace 2^k with A000108(k) in binary expansion of n.

Links

Table of n, a(n) for n=0..63.

Formula

G.f.: (1/(1 - x))*Sum_{k>=0} Catalan number(k)*x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Jul 23 2017

Example

11 = 1011_2, so a(11) = 1*1 + 1*1 + 0*2 + 1*5 = 7.

Crossrefs

Cf. A000108, A030308, A197433.

Other sequences that are built by replacing 2^k in binary representation with other numbers: A022290 (Fibonacci), A029931 (natural numbers), A059590 (factorials), A089625 (primes), A197354 (odd numbers).

Sequence in context: A072509 A269362 A321695 * A255573 A062298 A283371

Adjacent sequences: A197429 A197430 A197431 * A197433 A197434 A197435

Keyword

nonn,easy

Author

Philippe Deléham, Oct 15 2011

Status

approved